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1.
I I (, 1976). I :I I I I I I I (I) I I . I . , I I .
Euler solutions in the problem of the translatory-rotary motion of three rigid bodies
The present paper is a continuation of the article (Vidyakin, 1976) in which we proved the existence of Lagrange (triangle) solutions in the general problem of the translatory-rotary motion of three absolutely rigid bodies.In particular, we have found the conditions for the existence of Lagrange solutions in the case when all the bodies possess a symmetry with respect to three mutually perpendicular planes both in respect to the distribution of matter and in respect to the outward form. In this case the bodies effect simple translations along with the centres of the masses without rotation (in Lyapunov's system of coordinates).If the rigid bodies possess a symmetry in respect to the axis and to the plane, perpendicular to this axis, then the Lagrange solutions of the three floats (Duboshin, 1973), three spokes (Kondurar, 1974), three shafts (Vidyakin, 1976) types are admitted, as well as the solutions in the cases of combinations of the float, spoke and shaft-bodies (Vidyakin, 1976).Those solutions exist of certain conditions, imposed on the structure, orientation and rotation of the bodies, are observed.In the general case (there) exist particular solutions which we have termed as Near-Lagrangian.The present paper is to prove the existence of Euler (rectilinear) solutions in the problem of the translatory-rotary motion of three rigid bodies, assuming that the elementary particles of the rigid bodies are mutually attracted according to the Newtonian law.In particular, we have found the conditions for the existence of Euler solutions in the case when all the bodies possess a symmetry in respect to three mutually perpendicular planes both in respect to the distribution of matter and in respect to the outward form. In this case the bodies are so disposed in the uniformly rotating coordinate system that two symmetry planes concur while the centres of the masses are disposed on one straight line.In particular, if the bodies possess a symmetry in respect to the axis and to the plane perpendicular to this axis, then the Euler solutions of the three floats (Duboshin, 1973), three spokes, three shafts types as well as solutions in the cases of combinations of float-, spoke- and shaft-bodies and spheres, either homogeneous or possessing a spherically symmetric distribution of densities, are admitted.The paper gives exact solutions for the cases when the attraction force function of the bodies has an approximate expression.相似文献
2.
, (DM) (RM). , DM RM N
e
= n
e
ds. M
e
= n
e
H cos ds ; . Lerche (1970a, b) , DM RM N
e
M
e
. . 相似文献
3.
, . , , . , , -, This article investigates the dynamics of a system for damping the nutating motion of a spin-stabilized satellite. The equations of motion of the satellite-damper system are derived omitting consideration of the influence of external torques. The conditions of stability of the stationary spinning are obtained and the optimal parameters of the satellite and the damper ensuring a maximal rate of damping of the nutation motion are determined. 相似文献
4.
The gravity potential of an arbitrary bodyT is expanded in a series of spherical harmonics and rigorous evaluations of the general termV
n
of the expansion are obtained. It is proved thatV
n
decreases on the sphere envelopingT according to the power law if the body structure is smooth. For a body with analytic structure,V
n
decreases in geometric progression. The exactness of these evaluations is proved for bodies having irregular and analytic structures. For the terrestrial planetsV
n
=O (n
–5/2).
I I V n IV n I . . IV n I . I. IV n =O(n –5/2 )相似文献
5.
Г. С. Бисноватый-коган 《Astrophysics and Space Science》1973,22(2):293-306
. , , .. . . , (, ) . 相似文献
6.
, kT
b
mc
2 . . , , . E
–5, - E
2, mc
2(kT
/mc
2)1/7. , (>2.105
cm
–3) . , -, , . 相似文献
7.
, , , , . , , . , , - - ( , ..). - . 相似文献
8.
, . , , . . . . . , , . 相似文献
9.
A limiting case of the problem of three bodies (m
0,m
1,m
2) is considered. The distance between the bodiesm
0 andm
1 is assumed to be much less than that between their barycenter and the bodym
2 so that one may use Hill's approximation for the potential of interaction between the bodiesm
1 andm
2. In the absence of resonant relations the potential, double-averaged by the mean longitudes ofm
1 andm
2, describes the secular evolution of the orbits in the first approximation of the perturbation theory.As Harrington has shown, this problem is integrable. In the present paper a qualitative investigation of the evolution of the orbits and comparison with the analogous case in the restricted problem are carried out.The set of initial data is found, for which a collision between the bodiesm
0 andm
1 takes place.The region of the parameters of the problem is determined, for which plane retrograde motion is unstable.In a special example the results of approximate analysis are compared with those of numerical integration of the exact equations of the three body problem.
m 0,m 1,m 2. , m 0 m 1. m 2, m 1 m 2 m 1 m 2 . , . . , m 0 m 1. , . .相似文献
10.
К. Г. Иванов 《Astrophysics and Space Science》1974,31(2):277-285
=qm . . ¶, I . — , ¶, 5. , . : , , . =ah 4. . . , -, ( ). . 相似文献
11.
, . , . . , (, ). , ( , ). 相似文献
12.
Г. А. Гурзадян 《Astrophysics and Space Science》1977,46(2):471-484
, , , , ,S
, , , S
Mg. , . , . , ( , ..). B5 B0; (<1%). 相似文献
13.
Yu. I. Neshpor A. A. Stepanian V. P. Fomin S. A. Gerasimov B. M. Vladimirsky Yu. L. Ziskin 《Astrophysics and Space Science》1979,61(2):349-355
The period of very high energy (E>2×1012 eV) gamma-ray emission of Cyg X-3 by using the data of observations of the source made during 6 years, 1972–1977, was specified. The value of the period is equal to 0.199 683±1×10–6 days. Phase histogram reveals two peaks, one lagging the other by 0.6 of the period. The averaged 6 year data amounts to 1.8×10–10 quanta cm–2 s–1 (peak intensity). It corresponds to luminosity of about 1.2×1037 erg s–1 if one assumes that an emission is isotropical and the distance is equal to 10 kpc.
- E>2×1012 Cyg X-3 . 1972–1977 . - T=0,199 683 ±10–6 . , 0,6 . 1,8×10–10 –2 –1 ( ), 1,2×1037 / 10 .相似文献
14.
I I I : Mgas<0.04 Mcor. - . , . 相似文献
15.
. - . . , . - . - , , , -. ., , .
English translation will appear in the next issue ofAstrophys. Space Sci.
Receipt delayed by postal strike in Great Britain 相似文献
The structure of rotating magnetic polytropes is considered in Roche approximation. Investigation of the influence of poloidal as well as toroidal magnetic fields on the conditions of the beginning of matter outflow due to rotational instability is carried out. The influence of the turbulent convection and twisting of magnetic force-lines on the time of smoothing of differential rotation is considered. The estimate of the magneto-turbulence energy generated by differential rotation is presented. Both maximum possible energy output and duration of the quasi-statical evolution phase up to the appearance of hydrodynamic instability due to the effects of general relativity are calculated for supermassive magnetic polytropes of index three with uniform or differential rotation. The radius-mass relation is obtained for supermassive differentially-rotating magnetic polytropes referring to the longest part of the quasi-statistical evolution stage; some consequences are pointed out, including the period-luminosity relation.The evolution of the considered models of supermassive rotating magnetic polytropes with different character of rotation and different geometry of a magnetic field is discussed.The results obtained are summarized in the last section.
English translation will appear in the next issue ofAstrophys. Space Sci.
Receipt delayed by postal strike in Great Britain 相似文献
16.
В. А. Гаген-Торн 《Astrophysics and Space Science》1980,73(2):279-294
J 287 1972–1976. , . . J ( ), () . (0=80°) . J 287 ¶ . p=42.8%, 0=101°. (50%). 相似文献
17.
The problem of stability of the equilibrium points (the libration points) in the problem of motion of a mass point in the neighbourhood of a rotating triaxial ellipsoid is investigated in the strict sense.In the plane of parameters, depending on the form and dynamical characteristics of the ellipsoids, the regions of stability and instability of the libration points are obtained.It is shown that the libration points of the ellipsoids, the form and dynamical characteristics of which are close to the planets of the solar system, are stable.
( ) . , , . , , , .相似文献
18.
, () , , ( =2) , . (, , ). ( =0,5) . 相似文献
19.
Evolutionary tracks of 0.9M
, 0.7M
and 0.6M
models for Population II stars have been computed in the post-red giant phase. The stars are initially composed of a helium core containing a mass fraction equal to 0.9 and of a hydrogen-rich envelope. They represent hypothetical remnants of stars after substantial mass loss in previous evolutionary phases or/and at the helium flash.u 0,9M
, 0,7M
0,6M
. , 90% , . , .Riassunto È stata calcolata per modelli di stelle di 0,9M
, 0,7M
e 0,6M
di Popolazione II l'evoluzione successiva allo stadio di gigante rossa. Inizialmente i modelli constano di un nucleo di elio contenente il 90% della massa totale e di un inviluppo idrogenico. Essi possono interpretarsi come i resti di stelle che abbiano perso una frazione di massa considerevole in fasi evolutive precedenti, o all'innesco violento dell'elio al centro. 相似文献
20.
, , . . ( I), ( II). I , () . -, . , , (R/R
i)2/3, R/R
i- . ( II) . , . , , , . , . , , . , , - , , . , , , , . , . . . 1969 . 相似文献